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Lecture
Direct Methods for Linear Systems of Equations
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Related lectures (41)
Linear Systems Resolution
MOOC: Numerical Analysis for Engineers
Summarizes methods for resolving linear systems, including Gaussian elimination and LU decomposition.
Linear Systems: Chapters 4, 5, 6
Explores the link between linear systems and optimization through elimination and LU decomposition.
Linear Systems: LU Factorization with Pivoting
Explains the Gaussian elimination algorithm with pivoting and LU factorization for linear systems.
Floating Point Numbers: LU Decomposition and Errors
Explores floating point numbers, LU decomposition, errors, and matrix properties.
LU Decomposition Algorithm
MOOC: Linear Algebra (Part 1)
Covers the LU decomposition algorithm, transforming a matrix into L and U.
Linear Algebra Review
Covers the basics of linear algebra, including matrix operations and singular value decomposition.
LU Decomposition: Linear Systems Applications
MOOC: Linear Algebra (Part 1)
Covers the LU decomposition method applied to linear systems, presenting the system in two steps.
LU Factorization Criteria
Explores the conditions for LU factorization without permutation and diagonal dominance in matrices.
Decomposition LLT: Cholesky
MOOC: Numerical Analysis for Engineers
Covers the Cholesky decomposition of a symmetric positive definite matrix and its applications.
Linear Systems: Choleski Factorisation
Covers the Choleski factorisation method for solving linear systems efficiently.
Chaos and Lyapunov Exponents: Analyzing Predictability
Covers Lyapunov exponents, chaos measurement, and perturbation analysis in dynamical systems.
Finite Elements: Elasticity and Variational Formulation
Explores finite element methods for elasticity problems and variational formulations, emphasizing admissible deformations and numerical implementations.
Factorisation LU
Explains Gaussian elimination and LU factorization for solving linear systems of equations.
Cholesky Factorization: Theory and Algorithm
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Explores the Cholesky factorization method for symmetric positive definite matrices.
Linear Systems: Diagonal and Triangular Matrices, LU Factorization
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Covers linear systems, diagonal and triangular matrices, and LU factorization.
Thomas algorithm, accuracy of direct methods
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Explores the Thomas algorithm for tridiagonal systems and the accuracy of direct methods in numerical computations.
Numerical Analysis: Direct Methods for Linear Systems
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Covers direct methods for solving linear systems in numerical analysis.
Direct Methods for Solving Linear Equations
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Explores direct methods for solving linear equations and the impact of errors on solutions and matrix properties.
Matrix Factorizations: LU Decomposition
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Introduces LU decomposition for efficient linear equation solving using matrix factorization.
Linear Systems: Direct Methods
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Explores linear systems, direct methods, Gauss elimination, LU decomposition, and computational complexity.
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